Mixing of pseudoscalar-baryon and vector-baryon in the $J^P=1/2^-$ sector and the $N^*$(1535) and $N^*$(1650) resonances

TL;DR

This paper investigates the nature of the $N^*(1535)$ and $N^*(1650)$ resonances by modeling meson-baryon interactions with pseudoscalar and vector mesons, fitting to experimental data, and successfully reproducing observed properties.

Contribution

It introduces a coupled channels approach mixing pseudoscalar and vector meson-baryon states to describe the $J^P=1/2^-$ sector, providing new insights into the structure of the $N^*$ resonances.

Findings

Identified two poles corresponding to $N^*(1535)$ and $N^*(1650)$.

Achieved good agreement with experimental branching ratios.

Predicted cross sections consistent with experimental data.

Abstract

We study the meson-baryon interaction with $J^P=1/2^-$ using the hidden-gauge Lagrangians and mixing pseudoscalar meson-baryon with the vector meson-baryon states in a coupled channels scheme with $\pi N$, $\eta N$, $K\Lambda$, $K\Sigma$, $\rho N$ and $\pi \Delta$ (d-wave). We fit the subtraction constants of each channel to the $S_{11}$ partial wave amplitude of the $\pi N$ scattering data extracted from experimental data. We find two poles that we associate to the $N^*(1535)$ and the $N^*(1650)$ resonances and show that the subtraction constants are all negative and of natural size. We calculate the branching ratios for the different channels of each resonance and we find a good agreement with the experimental data. The cross section for the $\pi^- p \to \eta n$ scattering is also evaluated and compared with experiment.